Let Xn and Yn be two series of real numbers such that Xn<Yn for all n>N.

Show that a)lim inf Xn<lim inf Ynb)lim supXn<lim sup Yn

Jan 29th 2010, 10:33 PM

tonio

Quote:

Originally Posted by hebby

Let Xn and Yn be two series of real numbers such that Xn<Yn for all n>N.

Show that a)lim inf Xn<lim inf Ynb)lim supXn<lim sup Yn

Both inequalities are false: $\displaystyle \frac{n-1}{n}<\frac{n+1}{n}\,\,\,\forall\,\,n\in\mathbb{N}$, but there's equality in (a) and in (b) since the limit exists in both cases and is thus equal to the lower and upper limits.